Whatever the pressure-puncture relationship actually is, it is totally dwarfed by the choice of tire material/construction. The tire pressure choice is for handling characteristics, comfort and pinch-flat resistance. If you want to significantly increase puncture resistance, you do it by choosing a different tire, not by changing the pressure :-).
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AngeloJul 11 '12 at 15:15

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Are you referring to "thorn-penetration-mechanism", for instance, if a "harder" tire would be penetrated easier than a more "soft (not-so-inflated)" one?
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heltonbikerJul 11 '12 at 19:23

@heltonbiker sorry I am not familiar with technical details. From a layman perspective I want to know whether high pressured inner-tube will increase the chance of puncture or not
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Dinesh P.R.Jul 12 '12 at 5:08

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A high pressured inner tube? Like buy a tube that can take more pressure? that wont do anything. Pumping a tire up regardless of the tube's rating will reduce pinch-flats (snake bites) tremendously! And since I started riding super high PSI, I get less glass sticking to the tires and have not had a flat from glass in decades. Thorns? those will get you regardless of your PSI.
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BillyNairJul 12 '12 at 6:34

2 Answers
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It's not going to be directly proportional. Leaving aside the quality of the tyre and what it will be rated for, the shape of the graph is likely to be a U shape:

at the lower pressures the tube will be susceptible to puncture because it cannot repel sharps adequately, in addition really low pressures might let you trap the tube between the road and the rim.

as the pressure increases, the tube and tyre will combine to actively repel sharps: the external object will need more and more pressure and exertion to break through, so becomes less and less likely to be able to do so

at some point, though, the tube's pressure becomes so high, that the risk of a blowout increases: flaws in the tyre, the tube, especially around the valve, are more likely to be exploited, also that collisions e.g. with potholes, will be harder to accommodate.

It's not going to be as simple as that, but might work as a general rule.

Pressure does have effect a big effect on pinch flats. The more pressure in your tire, the less it will deform when you hit a bump (or the very evil train tracks). If if can't deform enough to pinch the tube, no flat. As the pressure decreases, the amount of force required to pinch also decreases. I'll drop some pressure for rainy wet roads, but I'll be more careful about things that go bump when I do.

That said, don't exceed the manufacture's (both tire and rim) max or min pressure. Worth keeping in mind that 110 lbs put in during the cool morning will be quite a bit higher as the sun beats halfway through a four hour ride.

Conversely, your tube can lose pressure for many reasons as well. Fill it during a flat change with CO2 during a hot day and you may notice it being really low the next morning.